For comparison, your old 3-speed had a range of 178%:

How it works

The four-speed hub has planetary gearing with a unity ratio and three increase ratios. Its operation is very similar to that of gears 5 through 8 of the Nexus 8-speed hub. A more detailed description is provided in another article on this site.

The internal mechanism of these hubs is complicated, and the usual repair is to replace it in its entirety. We have rebuilding instructions for both the freewheeling and coaster-brake versions of the hub, translated from the German versions, which were the only ones we could find online. The procedure given does not include information on timing the compound planet gears. Thanks go to Patricia Morris for pointing this out and for the photo below. The red arrow points to the timing mark. The marks on all three gears must point directly outward.

The right-hand hub bearing cup is vulnerable to damage from water contamination. Better lubrication is recommended to forestall this problem and to make cleaning and rebuilding easier.

Shimano lists the overlocknut distance of the 4-speed freewheeling brake hubs as 130 mm, as sold -- see Shimano's overlocknut spacing chart -- though also 123.5 mm and 127 mm, in its rebuilding instructions for the freewheeling/Rollerbrake version.
If not using a Rollerbrake, it is possible to reduce the overlocknut distance by using a thinner lockwasher, as described on the Rollerbrakes page.

The 4-speed hub uses the same cassette joint as the 7-speed hub.

The shift lever for the 4-speed hub may be unavailable, but the cable pull for the shift levers for Shimano 7-speed and 8-speed internal-gear hubs is close enough in the lowest 4 gears that these shifters can be used with the 4-speed.

The 4-speed hub has been sold with an automatic, electronic shifting system.

Information on the Shimano site about all these hubs may be found with this search. The table below includes rebuilding information not available on the Shimano site. The parts lists and exploded drawings are in the list which the links bring up -- same as the seach just mentioned.